I’ve been thinking about this lately too, for my own funeral (which hopefully won’t be for another 200 years!). In some religions, the funeral is necessary to properly send the deceased to the afterlife. In many others, it’s just a way of organizing our grief and making a spiritual experience out of it. But what is a funeral to an atheist?
In one sense, it makes no difference to me whether my family wants to talk religion at my funeral. I’m dead. There’s no afterlife, no consequence. But as a secular humanist, I have to disagree—My life is my legacy. What I am and what I do in the short time that I’m here is all that I can pass on to future generations. If my life is memorialized in a religious service… well it defeats the purpose.
I’ve already decided on one thing I can do—Have my body donated to science.
Anyway, to answer your question, I would focus my words on remembering the life of the person. Talk about what he/she has accomplished, how he/she has touched your life. Remember them for what they have done. Religion at funerals only acts to relieve grief (‘he/she is in a better place’ and such). If you want to relieve grief, try and talk about how the world is a better place for what he/she has done.
Sure, it takes a little more thought than the typical ‘God bless’ and all, but if you ask me, a little more thought is just what this place needs.